Counterexamples in TopologyOver 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Extensive collection of problems and exercises, correlated with examples. Bibliography. 1978 edition. 
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Review: Counterexamples in Topology
User Review  Stephen  GoodreadsAs the title states, this book provides counterexamples in topology (that you were probably too lazy to come up with). Some of the examples were very critical in understanding topology at the ... Read full review
Review: Counterexamples in Topology
User Review  psb  GoodreadsI might have debated whether to give this 4 or 5 stars if it had been a +$50 math book, but at $10, "the choice (function) is clear ..." Read full review
Contents
General Introduction  3 
Filters  9 
Compactnesa  18 
Connectedness  28 
Finite Discrete Topology  41 
EitherOr Topology  48 
Euclidean Topology  56 
One Point Compactiﬁcation Topology  63 
StoneCech Compactiﬁcation  129 
StoneCech Compactiﬁcation of the Integers  132 
Novak Space  134 
Strong Ultraﬁlter Topology  135 
Single Ultraﬁlter Topology  136 
Nested Rectangles  137 
The Inﬁnite Broom  139 
The Integer Broom  140 
Uncountable Discrete Ordinal Space  70 
Nested Interval Topology  76 
Relatively Prime Integer Topology  82 
Indiacrete Rational Extension of R  88 
Deleted Diameter Topology  94 
HalfDisc Topology  96 
Irregular Lattice Topology  97 
Arens Square  98 
Simpliﬁed Arens Square  100 
Metrizahle Tangent Disc Topology  103 
Michaels Product Topology  105 
Tychonof f Plank  106 
Alexandrof f Plank  107 
Dieudonne Plank  108 
Tychonof f Corkscrew  109 
Hewitts Condensed Corkscrew  111 
Thomas Plank  113 
Weak Parallel Line Topology  114 
Concentric Circles  116 
Appert Space  117 
Maximal Compact Topology  118 
Minimal Hausdorff Topology  119 
Alexandrof f Square  120 
Z  121 
Uncountahle Products of Z+  123 
Baire Product Metric on R  124 
I 125 106 O9 X I  126 
Helly Space  127 
C01 128 109 Box Product Topology on R  128 
The Inﬁnite Cage  141 
Bernsteins Connected Sets  142 
Roys Lattice Space  143 
Cantors Leaky Tent  145 
A PseudoArc  147 
Millers Biconnected Set  149 
Wheel without Its Hub  150 
Bounded Metrics  151 
Sierpinskis Metric Space  152 
Duncans Space  153 
Cauchy Completion  154 
The Post Ofﬁce Metric  155 
Radial Interval Topology  156 
Bings Discrete Extension Space  157 
Fur Ill METIIZATION THEORY Conjectures and Counterexamples  161 
APPENDICES  183 
Special Reference Charts  185 
Separation Axiom Chart  187 
Compactness Chm  188 
Paracompactness Chart 090  191 
Disconnectedness Chart  192 
Metrizability Chart  193 
General Reference Chart  195 
Problems  205 
68  210 
Notes  213 
Bibliography  228 
236  
Common terms and phrases
acompact arc connected basis element basis neighborhood basis sets clearly closed set closed subset closure collectionwise normal completely normal completely regular continuous function converges countable local basis countably paracompact counterexample deﬁne deﬁnition denote dense subset denseinitself discrete topology disjoint open sets equivalent Euclidean topology extremally disconnected ﬁlter ﬁnd ﬁrst countable function f Hausdorff space homeomorphic induced topology interval topology limit point Lindelof locally compact locally connected metacompact metric space Moore space nonempty normal Moore space normal space open and closed open cover open interval open neighborhoods open set containing order topology ordinal space paracompact space path connected plane point ﬁnite reﬁnement product topology properties quasicomponent radius real line regular space satisﬁes screenable second category second countable set theory Show space is metrizable subspace tangent disc theorem topological space topology Example totally disconnected totally separated Tychonoff ultraﬁlters uncountable union unit interval Urysohn zero dimensional